Sung lyrical verse, especially in a rock&roll/blues context, can't ever be called "poetry" really, as it doesn't have the same mode of expression as anything written.
That being said, there are segments of spoken poetry, scattered all across the lyrics and songs of The Doors; a lot of midsegments of songs have simply spoken poetry fragments where Jim just recites (like When The Musics Over). Other songs are just recited (not sung) poems with music in the background, like the posthumously released poetry album An American Prayer. It certainly shows that Jim was a poet. A lot of live performances were also begun with poetic recitations.
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